Semidefinite programming
![The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.](/Images/godic/202502/10/Max_paraboloid.svg0511.png")
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (an objective function is a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.